The Poverty of the Stimulus (PoS) argument holds that children do not receive enough evidence to infer the existence of core aspects of
language, such as the dependence of linguistic rules on hierarchical phrase structure. We reevaluate one version of this argument using a Bayesian model of grammar induction, and show that a rational learner faced with typical child-directed input and without any initial language-specific biases could learn this dependency. This enables the learner to master aspects of syntax, such as the auxiliary fronting
rule in interrogative formation, even without having heard directly relevant data ( e.g., interrogatives containing an auxiliary in a relative clause in the subject NP). The hierarchical Bayesian framework is also applicable to other innateness questions involving core aspects of linguistic structure.